2.1. Price dynamics

The LPPL framework starts by assessing the dynamics of housing price (p_t), taking the following form: (1) where u_t is a drift term and dj represents a discontinuous jump with the dummy variable j that switches to j = 0 prior to the critical time and to j = 1 afterward. The component size equals κ ∈ (0, 1). After we assume rational expectations and no arbitrage condition, the price process would be a martingale: (2) where h_t ≡ E[dj/dt] is the crash hazard rate. We can obtain u_t = κh_t, meaning that rational traders accept the risk of a bubble crash if they earn high enough profits to compensate for the risk. Then, the stochastic differential equation of the price dynamics before the crash is the following ordinary differential equation: (3) with the following solution: (4)

2.2. Microscopic modeling of the crash

Johansen et al. [26] introduced a microscopic model for an individual trader’s behavior. Specifically, the authors assumed that individual agent i can be in one of two states: s_i ∈ {−1, +1}. The authors then postulated that agent i’s state is determined as follows: (5) where K is the tendency toward imitation, N(i) is the set of traders influencing agent i’s behavior, σ is the tendency toward idiosyncratic behavior, and G is a global influence term. ε_i is assumed to be independent and follows the standard normal distribution. The average state of the system is then defined as follows: (6) where I is the total number of individual traders in the system. The system’s susceptibility is defined as follows: (7) which quantifies the sensitivity of the average state of the system to a small global influence [26].

2.3. Log-periodic power law model

Johansen et al. [26] proposed a hierarchical diamond lattice structure for the network of traders. The first-order expansion of the general solution is as follows: (8) where A₀, A₁, ω, and ψ are constants. γ is the critical exponent of susceptibility, and K_c is a critical point: the susceptibility is finite when K < K_c, but goes to infinity as K gets closer to K_c (i.e., the value of K at the critical time t_c).

If we assume that K is a function of time t and evolves smoothly over time, K(t) can be approximated using a first-order Taylor expansion as follows: (9) where θ is a constant. Johansen et al. [26] posited that the crash hazard rate behaves the same with the susceptibility near the critical point, and the crash hazard rate approximates to the following: (10) where t precedes the critical time t_c (i.e., 0 < t < t_c). That is, h_t includes a component of power law singularity caused by noisy traders’ self-reinforcing herding behavior, i.e., α(t_c − t)^β−1, as well as an oscillating component caused by heterogeneous interactions between fundamentalists and trend chasers, i.e., γ cos[ω log(t_c − t) + φ]. The power law singularity embodies the positive feedback mechanism that is driven by self-reinforcing beliefs, whereas log-periodicity captures the tug-of-war between the two types of investors leading to large-scale volatility and singularity, or critical time t_c [25, 27].

By using the solution of ordinary differential equation in subsection 2.1 (Eq (4)), we obtain the following: (11) where B₀ > 0 is the log price at critical time, i.e., , B₁ < 0 is equal to the increase in log price before the critical time, C ∈ (B₁, −B₁) controls the magnitude of oscillations around the exponential trend, and ϕ ∈ [0, 2π] is a phase parameter.

3.1. Bubble detection

Bubbles are typically defined as explosive price growth. In our context, a bubble is defined as an accelerating price that is faster than exponential (super-exponential). The faster than exponential implies that the growth rate is increasing, indicating a positive feedback process that reinforces growth. To detect the presence of a bubble, we distinguish between (standard) exponential and super-exponential growth. The former is characterized by the logarithm of the price being linear in time, as follows: (12)

The most basic extension of Eq (12) that results in super-exponential growth is as follows: (13)

The null hypothesis is c = 0. If the price process is found not to follow standard exponential growth, it can then be described as super-exponential growth. The improvement in the goodness of fit resulting from the quadratic term is measured by the root mean square of residuals, which is RMS_1,i for standard exponential growth and RMS_2,i for super-exponential growth in Eqs (12) and (13), respectively, as follows: (14) where a higher D value indicates a higher likelihood that the null hypothesis will be rejected and the quadratic term qualifying a bubble regime is relevant. As a result, we consider housing prices to be growing at a super-exponential rate if D_i ≥ 25% and c > 0 hold. If p_t meets both conditions but p_t−1 does not, then time t is considered to represent the start of the bubble [28, 29].

3.2. Fitting the LPPL parameters

The basic form of the LPPL model presented in Eq (11) requires estimating seven parameters. We set the objective function for the parameter estimation as the squared sum of residuals between the observation and the predicted value of the LPPL model as follows: (15) where y_t and T denote the log of observed price at time t and the number of observations in the dataset, respectively.

Let f(t; β, t_c) = (t_c − t)^β and g(t; β, ω, t_c, ϕ) = (t_c − t)^β cos[ω log(t_c − t) + ϕ], and we then obtain the following optimization problem: (16) where the coefficients A, B, and C can be estimated using the ordinary least squares method given the four parameters β, ω, t_c, and ϕ.

Previous studies have reported that the conditions for a bubble regime include 0 < β < 1 and B < 0 [10, 11, 25, 27, 30]. Specifically, β < 1 ensures that the expected log price diverges at the critical time and β > 0 ensures that the log price remains finite at t_c. The two conditions ensure super-exponential growth toward the critical time (t_c), implying that the crash hazard rate accelerates over time. To examine the regime shift before and after policy implementation, we relax the upper constraint on β; that is, β < 1. For ω, if the log-periodic oscillations are too fast (large ω), then the model would overfit the random noises of the data. In contrast, if the log-periodic oscillations are too slow (small ω), they contribute to the trend too much, neglecting the real oscillations in this false trend. However, previous research has demonstrated that log-periodic oscillations are neither too fast nor too slow for financial crashes, e.g., ω = 6.36 ± 1.56 [31], and ω has been found around the boundaries. Therefore, we only restrict ω to be positive as ω > 0 is simply the frequency of the fluctuations during the bubble formation [11].

We estimate the four nonlinear parameters (β, ω, t_c, and ϕ) using the MPGA. The genetic algorithm (GA) references concepts from biology such as crossover and mutation when searching for optimal parameters. However, unlike the traditional GA, the MPGA generates multiple populations and each population is muted into hundreds of chromosomes, each of which represents a feasible solution for the four nonlinear parameters in the LPPL model. If the optimization criteria are not met, the algorithm creates new populations and restarts the search. As a result, the algorithm enhances prediction accuracy and minimizes the impact of other factors such as crossover and mutation probability. Moreover, the MPGA avoids the local-trap and premature convergence problems of the standard GAs [32]. The specific MPGA procedure to optimize nonlinear parameters is presented in S1 Appendix. In particular, we employ a modified MPGA to determine the optimal parameter values in the LPPL model. We first partition the sample space into subintervals to mitigate the impact of a specific sample interval and then use the MPGA to fit the LPPL model within each subinterval.

3.3. Lomb–Scargle spectral analysis and unit root tests

We test log-periodicity using Lomb–Scargle spectral analysis [13] to detect periodic oscillation in our irregularly sampled data. The Lomb–Scargle analysis returns a series of frequencies (ω) and associated periodograms (P(ω)) that represent the power of the frequencies. The frequency with the maximum power is taken as the least squares frequency (ω_Lomb). We perform the Lomb–Scargle analysis on detrended residuals as follows: (17)

Specifically, we estimate the power at frequency ω as follows: (18) where r_s(t) is the standardized r(t) and ν_i is the log of (t_c − t) for observation i; that is, ln(t_c − t). τ is the time delay which satisfies the following: (19)

In the LPPL framework, the log-periodic oscillations result from the cosine part in Eq (11). As a result, if no log-periodicity is evident in the residuals, the angular frequency (ω_Lomb) should be close to ω_LPPL. The two frequencies are considered to be close if the absolute value of their difference is less than 0.3 [33]. Moreover, the p-value for the null hypothesis that the data is nonperiodic at a given frequency ω is calculated as 1 − [1 − exp(−P(ω))]^M, where M is the number of test frequencies. M is determined as the number of independent frequencies which are approximated as −6.362 + 1.193T + 0.00098T² [34].

Furthermore, if the logarithmic price in the bubble regime is attributed to a deterministic LPPL component, a mean-reversal Ornstein–Uhlenbeck (OU) process can be used to model residuals [12]. The test for the OU property of residuals can be translated into an AR(1) test for the corresponding residuals. Therefore, we conduct unit root tests on the LPPL residuals employing augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests. Rejecting the null hypothesis suggests that residuals are stationary and compatible with the OU process in the residuals. The optimal lag for the ADF test is determined by the minimum Akaike information criterion, while the lag for the PP test is calculated as 12(n/100)^1/4 [35].

4.1 Risk of bubble crash

We use monthly data on the average house prices in China’s first-tier cities from June 2010 to February 2022, which are obtained from the WIND database. Table 1 presents the summary statistics of our data. All data are annualized log returns. The mean and standard deviation decreases during the postimplementation period, indicating decelerated price growth and reduced volatility. Moreover, both skewness and kurtosis increase significantly, suggesting a change in distribution following policy implementation. We conjecture that the summary statistics suggest a plausible link between policy implementation and the housing market.

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Table 1. Descriptive statistics.

https://doi.org/10.1371/journal.pone.0309483.t001

As noted previously, the tightened regulations appear to be effective in reducing volatility in the housing market. We use the LPPL model to examine the effectiveness of government policies. Using a 12-month moving average, we identify the start of the bubble in July 2015 as D_July2015 = 0.3819 and c_July2015 = 0.0696, while D_June2015 = 0.0947 and c_July2015 = 0.0457. The blue solid line in Fig 2 is an in-sample estimate from the beginning of the bubble, while the blue dashed line identifies the time of tightening policy implementation. Comparing data and model responses, we conclude that our model fits very well for the Chinese housing market.

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Fig 2. Log-periodic power law fit to the Chinese housing market bubble preceding the 2016 policy tightening.

The blue and red solid lines indicate in-sample fit and out-of-sample predictions, respectively. The black dotted line represents the housing price in China. The blue dashed line indicates the 2016 tightening policy implementation. The red dashed line indicates the critical time predicted by the log-periodic power law model.

https://doi.org/10.1371/journal.pone.0309483.g002

We then conduct a postmortem analysis of the late 1980s Tokyo real estate bubble to determine whether easing the constraints on β affects the model’s detection power. We choose the Tokyo real estate bubble because it bears a striking resemblance to the current Chinese real estate market. We assume that the Japanese real estate bubble began in January 1986 because D_January1986 = 0.3971 and c_January1986 = 0.3236, while D_December1985 = 0.2156 and c_December1985 = 0.2154. Fig 3 presents an in-sample estimate from the start of the bubble to the policy tightening that was implemented in July 1987. Comparing data and LPPL model responses, we conclude that our model also fits well for the Japanese housing market.

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Fig 3. Log-periodic power law fit to the Japanese housing market bubble preceding the 1987 tightening policy.

The blue and red solid lines indicate in-sample fit and out-of-sample predictions, respectively. The black dotted line represents the house price in Japan. The blue dashed line indicates the 1987 tightening policy implementation. The red dashed line indicates the critical time predicted by the log-periodic power law model.

https://doi.org/10.1371/journal.pone.0309483.g003

Table 2 summarizes the parameter estimates. For both housing markets, two parameters confirm a faster than exponential acceleration of log prices (i.e., B < 0 and 0.1 < β < 0.9) [12]. Consistent with previous studies [12, 31], the ω values are 8.92 and 7.57, respectively.

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Table 2. The best fit of log-periodic power law parameters.

https://doi.org/10.1371/journal.pone.0309483.t002

4.2 Policy impact

We then conduct out-of-sample forecasting for the post-implementation period, which is after October 2016 and July 1987 for China and Japan, respectively. Although the LPPL model indicates a critical time in the first half of 2017, market prices did not rapidly increase without the collapse of the bubble. This implies that the government policies that were implemented to curb a boom in the housing market were accurately timed. In contrast, after reaching its peak, Tokyo’s housing price index began to fall abruptly in November 1987, which is consistent with the critical time in Table 2. This suggests that the Bank of Japan’s tightened monetary policy caused a sharp decline in the growth of money supply, which triggered a housing market crash.

Despite similar credit loan restrictions, Figs 2 and 3 reveal different reactions from the Japanese and Chinese housing markets following policy implementation. We next investigate how LPPL parameters changed near the critical time, changing the end date of the in-sample estimation for the two housing markets to examine the sensitivity of the LPPL parameters.

Table 3 Panel A presents the MPGA estimates for the Chinese housing market. End time spans from two months prior to policy implementation to 11 months following implementation, from August 2016 to September 2017, to include information leakage and policy transmission near the implementation. Initially, prices exhibited upward acceleration with the coefficient B lower than zero. At the same time, the coefficient β < 1 reveals a faster than exponential acceleration of log prices until October 2016, supporting the argument that a housing bubble is evident and could burst soon. Prior to the 2016 tightening policy, the value of ω is between 8.92 and 12.91, which is consistent with existing literature [12, 31]. However, following policy implementation, the market abruptly changed and β became higher than one, rising from 0.8651 to 1.7375, indicating a reduced crash hazard rate. Parameter ω suddenly dropped to 0.86 in November 2016, implying the beginning of a new regime that is representative of a soft landing scenario. The empirical results validate the argument that government policies enacted to curb a housing market boom were accurately timed and the housing market transitioned to a soft landing state.

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Table 3. The best fit of log-periodic power law parameters near policy implementation.

https://doi.org/10.1371/journal.pone.0309483.t003

Panel B in Table 3 presents the MPGA estimates for the Japanese housing market. Apart from May 1987, all βs are lower than one, indicating an increasing crash hazard rate. A negative coefficient B and β below one, indicating upward acceleration, provide evidence that a bubble was developing and a crash was looming. All the warning signals reveal that a crash in less than three months was imminent. Specifically, t_c − t became significantly smaller after July 1987 and its average dropped from 2.58 months to 1.09 months after policy implementation. The critical time was primarily concentrated on late October and early November, which is approximately one month preceding the real crash.

4.3 Diagnostic tests

The Lomb–Scargle periodograms of the detrended residuals are presented in Fig 4. Each point in the Lomb–Scargle periodogram represents the highest peak and its associated angular log-frequency for a given detrended residual series. The red solid line presents the results for the Chinese housing market, and the blue dashed line indicates those for the Japanese housing market. The angular log-periodic frequencies associated with the highest Lomb peaks are 9.02 and 7.72, respectively. The p-values of Lomb–Scargle periodograms for Chinese and Japanese housing markets are 0.0362 and 0.0520, respectively. These angular frequencies are close to the values obtained with the parameter estimates that are summarized in Table 2.

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Fig 4. Lomb-Scargle periodograms for the Chinese and the Japanese housing markets.

The red solid line indicates the power of the house price in China at each frequency. The blue dashed line indicates that of the house price in Japan.

https://doi.org/10.1371/journal.pone.0309483.g004

Panel A of Table 4 presents the result of unit root tests for which the null hypothesis is that the time series has a unit root and is nonstationary for the Chinese housing market (We also test for homoscedasticity of the LPPL residuals since the ADF test requires that data be homoscedastic, failing to reject the null hypothesis of no heteroskedasticity in the LPPL residual series for Chinese and Japanese housing markets). According to the ADF test, the null hypothesis is rejected for all the series of residuals other than the four series with end times in September 2016, March 2017, May 2017, and August 2017. With the exception of November 2016, the null hypothesis is rejected for all the series of residuals according to the PP test. These findings collectively suggest that the LPPL residuals in the Chinese housing market do not have a unit root and are stationary. Panel B of Table 4 presents the results of unit root tests for the Japanese housing market. According to the ADF test, all the residual series except that with end times in June 1987 reject the null hypothesis. In addition, all the series reject the null hypothesis according to the PP test, indicating that the LPPL residuals in the Japanese housing market also do not have a unit root and exhibit stationarity. Therefore, we conclude that the LPPL residuals in both the Chinese and Japanese housing markets follow a mean-reverting OU process, revealing a key property of the LPPL model [11].

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Table 4. Unit root tests.

https://doi.org/10.1371/journal.pone.0309483.t004

Identifying a bubble using the LPPL model depends on two critical parameters such as β and ω; therefore, it is crucial to examine the sensitivity of the root mean square errors (RMSEs) of the fitted models to variations in these parameters. Fig 5 illustrates the sensitivity of the LPPL fit reported in Table 2 to variations in each of the four parameters (β, ω, ϕ, and t_c, in the case of China), revealing that the RMSE of the fitted model for China is not sensitive to small fluctuations in the chosen values for β, ω, ϕ, and t_c. We also conduct sensitivity analysis on the fitted model for the Japanese housing market. As shown in Fig 6, the fitted model for Japan is not sensitive to β, ω, ϕ, and t_c as well, indicating that the model for Japan is also not sensitive to small fluctuations in the four parameters.

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Fig 5. Sensitivity analysis of root mean square errors to the parameters of the log-periodic power law model for the Chinese housing market.

Figures A–D represent RMSE sensitivity to β, t_c, ω, and ϕ, respectively.

https://doi.org/10.1371/journal.pone.0309483.g005

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Fig 6. Sensitivity analysis of root mean square errors to the parameters of the log-periodic power law model for the Japanese housing market.

Figures A–D represent RMSE sensitivity to β, t_c, ω, and ϕ, respectively.

https://doi.org/10.1371/journal.pone.0309483.g006

4.4 Susceptibility

The next question we address is how to explain the different behavior of the Chinese and Japanese housing markets, given the similar credit loan restrictions. Specifically, we want to know what determines a market crash rather than a soft landing. Eq (2) indicates that the higher the probability of a crash is, the faster the price should grow to compensate investors for the increased risk of a crash in the market. In other words, increases in u_t are directly linked to increases in the crash hazard rate (h_t), which is strictly related to a system’s susceptibility. Susceptibility measures the ability of agents in a system to reach agreement (i.e., the probability that a large number of agents will take the same position simultaneously) and explains how the emergence of global synchronization from local imitation might cause a crash. The susceptibility of a market χ can be estimated by κh_-, which can be determined from the estimated LPPL parameters as follows: where the estimated κh_t can be negative, although, by definition, κ ∈ (0, 1) and the hazard rate should be positive. We approximate h_t in the LPPL model referencing Sornette [36].

A higher drift in a market in which bubbles are forming indicates that a system is extremely sensitive to even small global perturbation. In such cases, when the time approaches t_c, the crash hazard rate (i.e., the probability that a large number of agents will assume the same sell position simultaneously) rises, resulting in an imbalanced market unless prices decrease significantly, at which time prices explode and the probability of a smooth landing plummets to zero.

Therefore, we compare the market susceptibility of the housing markets of China, Japan, and South Korea. We include the South Korean housing market in this analysis for the following reason. Jang et al. [25] examined the real estate market in South Korea, providing evidence that the 2016 South Korean tightening policy was an effective tool for stabilizing housing prices and improving market conditions. However, the subsequent fiscal expansion implemented in November 2017, which was specifically aimed toward economically vulnerable groups—new employees, college graduates, newlyweds, senior citizens, and low-income earners—had no significant impact on the housing market.

Table 5 presents the estimated κh_t to measure market susceptibility, around time T (i.e., July 1987 for Japan, October 2016 for China, and October 2016 for South Korea). Different rates in Table 5 explain different reactions to tightening policy, revealing that κh_t is higher in Japan than China and South Korea, which indicates that the Japanese housing market is more vulnerable. The 1987 tightening policy shifted demand to the left, triggering a crash, because the Japanese housing market was extremely sensitive to global perturbations. In contrast, Chinese and Korean housing markets have a lower κh_t, indicating lower susceptibility when the tightening policy was implemented. Both markets were less sensitive to minor global fluctuations, the tendency to imitate was weaker, and no strong dominance of one state or position was evident among the agents. As a result, both markets switched to a soft landing state with a β greater than one. Furthermore, the low hazard rates and susceptibility help explain why the Korean market did not react to the 2017 fiscal expansion, as documented by Jang et al. [25].

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Table 5. Approximated hazard rate.

https://doi.org/10.1371/journal.pone.0309483.t005

In conclusion, our evidence indicates that demand-side policy should be implemented expediently when the system is not vulnerable to small global perturbations and there is no strong agreement among agents to be effective. Conversely, late implementation timing may exacerbate agents’ tendency to imitate others, increase the dominance of one position, and ultimately trigger a market crash.

4.5. Discussion on housing policies

We have shown that housing policies should be implemented with accurate timing with low (but not too low) susceptibility to facilitate a soft landing of the housing market bubble. However, the question remains: Is a soft landing after a housing bubble always good? Moreover, we should note that the Chinese housing market is not only influenced by investors’ speculative motives, which was the key concern of the 2016 tightening policy, but also by many other factors, including political ideology, social phenomena, geography, and others. Accordingly, in this subsection, we introduce several notable points when examining housing policies, especially in China.

The Chinese economy is transitioning to a market economy. Moreover, China is distinct from other transitional economies (e.g., Eastern European countries) in that it has only adopted the economic aspects of the market economy, in contrast to most other economies in transition that are fully transitioning to a path of Western liberalism [37]. Hence, we compare the housing market reaction to regulations in China and those in Eastern Europe. After liberalization, Eastern European countries experienced housing booms and busts in the past several decades, with macroprudential policies implemented, some of which have affected housing prices significantly, while others have not [38]. Such boom–bust cycles also occur in developed economies, significantly affected by monetary policies (e.g., interest rates and global liquidity) [39]. Consequently, the housing market fluctuations in Eastern Europe resemble those of mature market economies as, no matter whether they occur in developing or developed economies, housing markets in liberal countries experience bubbles and crashes following the implementation of macroeconomic or financial policies. In contrast, China has sought to avoid systemic risks originating from real estate boom–bust cycles to avoid a crash. As a socialist market economy, the Chinese economy could have successfully relieved the speculative mechanism in the housing market by imposing prudential requirements, monitoring real estate markets, and related approaches [40]. Likewise, the 2016 tightening policy that we focused on this study could also be accurately timed and effective due to state monitoring and market control. In summary, the Chinese housing market reaction to regulations differs from other economies in transition because of differing paths toward market economy development, and the continuing leadership of the Chinese Communist Party could have a significant influence on housing market stability that has been adequate enough to prevent housing prices from experiencing a hard landing.

We can cite cases of housing market soft landings from the history of other transitional countries. For example, the Czech Republic introduced or changed macroprudential policy instruments including the LTV, debt-service-to-income, and debt-to-income limits to reduce risks in the real estate market and mortgage financing from 2015 to 2022 [41]. These demand-side regulations resulted in a significant decrease in the number of new mortgage agreements, cooling down the Czech housing market without a price plummet [42]. Moreover, Vandenbussche et al. [38] found that changes in the minimum capital adequacy ratio (CAR) and marginal reserve requirements (MRRs) related to credit growth significantly decreased housing price inflation in countries in Central, Eastern, and Southeastern Europe (CESEE) during their sample period, which varies by country, ranging from the first quarter of 1997 to the first quarter of 2011. In particular, most of the countries had not experienced a housing price hard landing, indicating that the changes in the minimum CAR or MRRs related to credit growth helped the housing markets in CESEE countries to soft land following sharp price increases. These examples from other regions with transitioning economies again imply the importance of accurately timed policy implementation to prevent the hard landing of housing prices, which we demonstrate in the case of China’s 2016 tightening policy.

Meanwhile, concerns have been expressed that the efforts to cool down demand for properties such as China’s 2016 tightening policy only decrease the number of transactions, rather than property prices [42], resulting in a continuous increase in housing prices. Housing prices surge during a bubble build-up period, and can sometimes be decelerated by effective policy implementation, which we call a soft landing. The problem is that persistent price increases lead to a housing affordability issue wherein people cannot afford to buy a house because of overly high housing prices, excess demand, or scarce supply. Various efforts to alleviate housing unaffordability include supply-side intervention, demand-side intervention, rent/price control, anti-speculation, and multiple policies [43]. China’s 2016 tightening policy was a kind of anti-speculation policy that attempted to prevent super-exponential growth in housing prices. In this study, we argue that the soft landing following the tightening policy represented an ideal result, driving away short-term speculative investors and avoiding a crash. However, future studies may reconsider the effectiveness of China’s tightening policy by examining housing affordability.

Finally, we consider social housing, which is another significant aspect of the property market and housing policy. In transitional economies, real estate properties have been privatized or restored, the social housing sector has been downsized, and the remaining social housing is concentrated among the society’s most vulnerable groups [44]. Housing problems have been moved to the private sector, and most new houses are built by commercial providers in transitional countries and developed countries in Northwestern Europe [45]. Nevertheless, social housing still has many advantages; for example, it can lead to sustainable and balanced development, does not concentrate on central urban areas, and offers houses to socially vulnerable people that suffer from the housing affordability problem. Moreover, social housing directly or indirectly affects the commercial housing market in terms of price, supply, and demand [46]. Accordingly, policymakers must also consider the social housing sector. Specifically, it is preferable to consider the social housing sector to manage different prominent issues simultaneously when devising or evaluating real estate policy. In this sense, the Chinese government should initiate future policies to prevent a housing price crash and reconcile social problems for general social welfare.